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Journal articles on the topic 'Combinatorics on words'

Author: Grafiati

Published: 4 June 2021

Last updated: 11 June 2025

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1

Chen, Herman Z. Q., and Sergey Kitaev. "On universal partial words for word-patterns and set partitions." RAIRO - Theoretical Informatics and Applications 54 (2020): 5. http://dx.doi.org/10.1051/ita/2020004.

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Universal words are words containing exactly once each element from a given set of combinatorial structures admitting encoding by words. Universal partial words (u-p-words) contain, in addition to the letters from the alphabet in question, any number of occurrences of a special “joker” symbol. We initiate the study of u-p-words for word-patterns (essentially, surjective functions) and (2-)set partitions by proving a number of existence/non-existence results and thus extending the results in the literature on u-p-words and u-p-cycles for words and permutations. We apply methods of graph theory and combinatorics on words to obtain our results.

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2

Keränen, Veikko. "Combinatorics on Words." Mathematica Journal 11, no. 3 (2010): 358–75. http://dx.doi.org/10.3888/tmj.11.3-4.

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3

Carpi, Arturo, and Clelia De Felice. "Combinatorics on words." Theoretical Computer Science 412, no. 27 (2011): 2909–10. http://dx.doi.org/10.1016/j.tcs.2011.01.015.

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4

Allouche, J. P. "Algebraic Combinatorics on Words." Semigroup Forum 70, no. 1 (2004): 154–55. http://dx.doi.org/10.1007/s00233-004-0146-9.

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5

BUCCI, MICHELANGELO, SVETLANA PUZYNINA, and LUCA Q. ZAMBONI. "Central sets generated by uniformly recurrent words." Ergodic Theory and Dynamical Systems 35, no. 3 (2013): 714–36. http://dx.doi.org/10.1017/etds.2013.69.

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AbstractA subset $A$ of $ \mathbb{N} $ is called an IP-set if $A$ contains all finite sums of distinct terms of some infinite sequence $\mathop{({x}_{n} )}\nolimits_{n\in \mathbb{N} } $ of natural numbers. Central sets, first introduced by Furstenberg using notions from topological dynamics, constitute a special class of IP-sets possessing rich combinatorial properties: each central set contains arbitrarily long arithmetic progressions and solutions to all partition regular systems of homogeneous linear equations. In this paper we investigate central sets in the framework of combinatorics on words. Using various families of uniformly recurrent words, including Sturmian words, the Thue–Morse word and fixed points of weak mixing substitutions, we generate an assortment of central sets which reflect the rich combinatorial structure of the underlying words. The results in this paper rely on interactions between different areas of mathematics, some of which have not previously been directly linked. They include the general theory of combinatorics on words, abstract numeration systems, and the beautiful theory, developed by Hindman, Strauss and others, linking IP-sets and central sets to the algebraic/topological properties of the Stone-Čech compactification of $ \mathbb{N} $.

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6

Manea, Florin, and Dirk Nowotka. "TCS Special Issue: Combinatorics on Words – WORDS 2015." Theoretical Computer Science 684 (July 2017): 1–2. http://dx.doi.org/10.1016/j.tcs.2017.05.027.

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7

Lecroq, Thierry, and Svetlana Puzynina. "TCS special issue: Combinatorics on Words – WORDS 2021." Theoretical Computer Science 952 (March 2023): 113688. http://dx.doi.org/10.1016/j.tcs.2023.113688.

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8

BLANCHET-SADRI, F. "ALGORITHMIC COMBINATORICS ON PARTIAL WORDS." International Journal of Foundations of Computer Science 23, no. 06 (2012): 1189–206. http://dx.doi.org/10.1142/s0129054112400473.

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Algorithmic combinatorics on partial words, or sequences of symbols over a finite alphabet that may have some do-not-know symbols or holes, has been developing in the past few years. Applications can be found, for instance, in molecular biology for the sequencing and analysis of DNA, in bio-inspired computing where partial words have been considered for identifying good encodings for DNA computations, and in data compression. In this paper, we focus on two areas of algorithmic combinatorics on partial words, namely, pattern avoidance and subword complexity. We discuss recent contributions as well as a number of open problems. In relation to pattern avoidance, we classify all binary patterns with respect to partial word avoidability, we classify all unary patterns with respect to hole sparsity, and we discuss avoiding abelian powers in partial words. In relation to subword complexity, we generate and count minimal Sturmian partial words, we construct de Bruijn partial words, and we construct partial words with subword complexities not achievable by full words (those without holes).

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9

Lothaire, M. "Review of applied combinatorics on words." ACM SIGACT News 39, no. 3 (2008): 28–30. http://dx.doi.org/10.1145/1412700.1412706.

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10

de Luca, Aldo. "On the combinatorics of finite words." Theoretical Computer Science 218, no. 1 (1999): 13–39. http://dx.doi.org/10.1016/s0304-3975(98)00248-5.

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11

Fici, Gabriele, and Svetlana Puzynina. "Abelian combinatorics on words: A survey." Computer Science Review 47 (February 2023): 100532. http://dx.doi.org/10.1016/j.cosrev.2022.100532.

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12

Berstel, Jean, and Dominique Perrin. "The origins of combinatorics on words." European Journal of Combinatorics 28, no. 3 (2007): 996–1022. http://dx.doi.org/10.1016/j.ejc.2005.07.019.

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13

ILIE, LUCIAN, SHENG YU, and KAIZHONG ZHANG. "WORD COMPLEXITY AND REPETITIONS IN WORDS." International Journal of Foundations of Computer Science 15, no. 01 (2004): 41–55. http://dx.doi.org/10.1142/s0129054104002297.

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With ideas from data compression and combinatorics on words, we introduce a complexity measure for words, called repetition complexity, which quantifies the amount of repetition in a word. The repetition complexity of w, R (w), is defined as the smallest amount of space needed to store w when reduced by repeatedly applying the following procedure: n consecutive occurrences uu…u of the same subword u of w are stored as (u,n). The repetition complexity has interesting relations with well-known complexity measures, such as subword complexity, SUB , and Lempel-Ziv complexity, LZ . We have always R (w)≥ LZ (w) and could even be that the former is linear while the latter is only logarithmic; e.g., this happens for prefixes of certain infinite words obtained by iterated morphisms. An infinite word α being ultimately periodic is equivalent to: (i) [Formula: see text], (ii) [Formula: see text], and (iii) [Formula: see text]. De Bruijn words, well known for their high subword complexity, are shown to have almost highest repetition complexity; the precise complexity remains open. R (w) can be computed in time [Formula: see text] and it is open, and probably very difficult, to find fast algorithms.

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14

Reshetnikov, Ivan Andreevich. "Combinatorics on words, facrordynamics and normal forms." Chebyshevskii sbornik 22, no. 2 (2021): 202–35. http://dx.doi.org/10.22405/2226-8383-2021-22-2-202-235.

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15

de Luca, Aldo. "Sturmian words: structure, combinatorics, and their arithmetics." Theoretical Computer Science 183, no. 1 (1997): 45–82. http://dx.doi.org/10.1016/s0304-3975(96)00310-6.

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16

Melançon, Guy. "Combinatorics of Hall trees and Hall words." Journal of Combinatorial Theory, Series A 59, no. 2 (1992): 285–308. http://dx.doi.org/10.1016/0097-3165(92)90070-b.

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17

GOČ, DANIEL, DANE HENSHALL, and JEFFREY SHALLIT. "AUTOMATIC THEOREM-PROVING IN COMBINATORICS ON WORDS." International Journal of Foundations of Computer Science 24, no. 06 (2013): 781–98. http://dx.doi.org/10.1142/s0129054113400182.

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We describe a technique for mechanically proving certain kinds of theorems in combinatorics on words, using finite automata and a software package for manipulating them. We illustrate our technique by applying it to (a) solve an open problem of Currie and Saari on the lengths of unbordered factors in the Thue-Morse sequence; (b) verify an old result of Prodinger and Urbanek on the regular paperfolding sequence; (c) find an explicit expression for the recurrence function for the Rudin-Shapiro sequence; and (d) improve the avoidance bound in Leech's squarefree sequence. We also introduce a new measure of infinite words called condensation and compute it for some famous sequences. We follow up on the study of Currie and Saari of least periods of infinite words. We show that the characteristic sequence of least periods of a k-automatic sequence is (effectively) k-automatic. We compute the least periods for several famous sequences. Many of our results were obtained by machine computations.

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18

Klíma, Ondřej. "Piecewise testable languages via combinatorics on words." Discrete Mathematics 311, no. 20 (2011): 2124–27. http://dx.doi.org/10.1016/j.disc.2011.06.013.

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19

Giambruno, Antonio, and Mikhail Zaicev. "Polynomial identities and algebraic combinatorics on words." São Paulo Journal of Mathematical Sciences 10, no. 2 (2015): 219–27. http://dx.doi.org/10.1007/s40863-015-0034-0.

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20

Hàn, Hiệp, Marcos Kiwi, and Matías Pavez-Signé. "Quasi-random words and limits of word sequences." European Journal of Combinatorics 98 (December 2021): 103403. http://dx.doi.org/10.1016/j.ejc.2021.103403.

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21

Boyd, Rachael, and Richard Hepworth. "Combinatorics of injective words for Temperley-Lieb algebras." Journal of Combinatorial Theory, Series A 181 (July 2021): 105446. http://dx.doi.org/10.1016/j.jcta.2021.105446.

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22

Brlek, Srečko. "Interactions between Digital Geometry and Combinatorics on Words." Electronic Proceedings in Theoretical Computer Science 63 (August 17, 2011): 1–12. http://dx.doi.org/10.4204/eptcs.63.1.

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23

Currie, James D., and Cameron W. Pierce. "The Fixing Block Method in Combinatorics on Words." Combinatorica 23, no. 4 (2003): 571–84. http://dx.doi.org/10.1007/s00493-003-0034-z.

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24

Brlek, Srečko, Marc Chemillier, and Christophe Reutenauer. "Music and combinatorics on words: a historical survey." Journal of Mathematics and Music 12, no. 3 (2018): 125–33. http://dx.doi.org/10.1080/17459737.2018.1542055.

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25

DIEKERT, VOLKER, and ALEXEI MYASNIKOV. "GROUP EXTENSIONS OVER INFINITE WORDS." International Journal of Foundations of Computer Science 23, no. 05 (2012): 1001–19. http://dx.doi.org/10.1142/s0129054112400424.

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Non-Archimedean words have been introduced as a new type of infinite words which can be investigated through classical methods in combinatorics on words due to a length function. The length function, however, takes values in the additive group of polynomials ℤ[t] (and not, as traditionally, in ℕ), which yields various new properties. Non-Archimedean words allow to solve a number of interesting algorithmic problems in geometric and algorithmic group theory. There is also a connection to logic and the first-order theory in free groups (Tarski Problems). In the present paper we provide a general method to use infinite words over a discretely ordered abelian group as a tool to investigate certain group extensions for an arbitrary group G. The central object is a group E (A, G) which is defined in terms of a non-terminating, but confluent rewriting system. The groupG as well as some natural HNN-extensions of G embed into E (A, G) (and still "behave like" G), which makes it interesting to study its algorithmic properties. In order to show that every group G embeds into E (A, G) we combine methods from combinatorics on words, string rewriting and group theory.

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26

Teimoori Faal, Hossein. "A Multiset Version of Even-Odd Permutations Identity." International Journal of Foundations of Computer Science 30, no. 05 (2019): 683–91. http://dx.doi.org/10.1142/s0129054119500163.

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In this paper, we present a multiset analogue of the even-odd permutations identity in the context of combinatorics of words. The multiset version is indeed equivalent to the coin arrangements lemma which is a key lemma in Sherman’s proof of Feynman’s conjecture about combinatorial solution of Ising model in statistical physics. Here, we give a bijective proof which is based on the standard factorization of a Lyndon word.

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27

Vuillon, Laurent. "A Characterization of Sturmian Words by Return Words." European Journal of Combinatorics 22, no. 2 (2001): 263–75. http://dx.doi.org/10.1006/eujc.2000.0444.

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28

Zhi-Xiong, Wen, and Wen Zhi-Ying. "Some Properties of the Singular Words of the Fibonacci Word." European Journal of Combinatorics 15, no. 6 (1994): 587–98. http://dx.doi.org/10.1006/eujc.1994.1060.

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29

Blasiak, P., G. H. E. Duchamp, A. Horzela, K. A. Penson, and A. I. Solomon. "Heisenberg–Weyl algebra revisited: combinatorics of words and paths." Journal of Physics A: Mathematical and Theoretical 41, no. 41 (2008): 415204. http://dx.doi.org/10.1088/1751-8113/41/41/415204.

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30

Dai, Wan Ji, Kebo Lü, and Jun Wang. "Combinatorics on words in symbolic dynamics: The quadratic map." Acta Mathematica Sinica, English Series 24, no. 12 (2008): 1985–94. http://dx.doi.org/10.1007/s10114-008-7490-8.

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31

Chuan, Wai-Fong, Fang-Yi Liao та Fei Yu. "Markov word patterns and a relation on α-words". Discrete Applied Mathematics 214 (грудень 2016): 63–87. http://dx.doi.org/10.1016/j.dam.2016.05.032.

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32

Mahalingam, Kalpana, Anuran Maity, and Palak Pandoh. "Rich words in the block reversal of a word." Discrete Applied Mathematics 334 (July 2023): 127–38. http://dx.doi.org/10.1016/j.dam.2023.03.013.

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33

Bēts, Raivis, and Alexander Šostak. "Fuzzy Approximating Metrics, Approximating Parametrized Metrics and Their Relations with Fuzzy Partial Metrics." Mathematics 11, no. 15 (2023): 3313. http://dx.doi.org/10.3390/math11153313.

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We generalize the concept of a fuzzy metric by introducing its approximating counterpart in order to make it more appropriate for the study of some problems related to combinatorics on words. We establish close relations between fuzzy approximating metrics in the case of special t-norms and approximating parametrized metrics, discuss some relations between fuzzy approximating metrics and fuzzy partial metrics, as well as showing some possible applications of approximating parametrized metrics in the problems of combinatorics on words.

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34

Gutin, Gregory, Toufik Mansour, and Simone Severini. "A characterization of horizontal visibility graphs and combinatorics on words." Physica A: Statistical Mechanics and its Applications 390, no. 12 (2011): 2421–28. http://dx.doi.org/10.1016/j.physa.2011.02.031.

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35

Louck, James D. "Problems in combinatorics on words originating from discrete dynamical systems." Annals of Combinatorics 1, no. 1 (1997): 99–104. http://dx.doi.org/10.1007/bf02558466.

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36

Dai, Wan Ji, Kebo Lü, and Jun Wang. "Combinatorics on words in symbolic dynamics: the antisymmetric cubic map." Acta Mathematica Sinica, English Series 24, no. 11 (2008): 1817–34. http://dx.doi.org/10.1007/s10114-008-7489-1.

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37

Bucci, Michelangelo, Aldo de Luca, Alessandro De Luca та Luca Q. Zamboni. "On θ-episturmian words". European Journal of Combinatorics 30, № 2 (2009): 473–79. http://dx.doi.org/10.1016/j.ejc.2008.04.010.

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38

de Luca, Aldo, and Luca Q. Zamboni. "Involutions of epicentral words." European Journal of Combinatorics 31, no. 3 (2010): 867–86. http://dx.doi.org/10.1016/j.ejc.2009.07.002.

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39

Bašić, Bojan. "On highly potential words." European Journal of Combinatorics 34, no. 6 (2013): 1028–39. http://dx.doi.org/10.1016/j.ejc.2013.02.006.

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40

Barbero, Florian, Guilhem Gamard, and Anaël Grandjean. "Quasiperiods of biinfinite words." European Journal of Combinatorics 85 (March 2020): 103046. http://dx.doi.org/10.1016/j.ejc.2019.103046.

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41

Ambrož, Petr, Zuzana Masáková, and Edita Pelantová. "Morphisms generating antipalindromic words." European Journal of Combinatorics 89 (October 2020): 103160. http://dx.doi.org/10.1016/j.ejc.2020.103160.

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42

MIGNOSI, FILIPPO. "STURMIAN WORDS AND AMBIGUOUS CONTEXT-FREE LANGUAGES." International Journal of Foundations of Computer Science 01, no. 03 (1990): 309–23. http://dx.doi.org/10.1142/s0129054190000229.

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If x is a rational number, 0<x≤1, then A(x)c is a context-free language, where A(x) is the set of factors of the infinite Sturmian words with asymptotic density of 1’s smaller than or equal to x. We also prove a “gap” theorem i.e. A(x) can never be an unambiguous co-context-free language. The “gap” theorem is established by proving that the counting generating function of A(x) is transcendental. We show some links between Sturmian words, combinatorics and number theory.

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43

Blanchet-Sadri, F. "Primitive partial words." Discrete Applied Mathematics 148, no. 3 (2005): 195–213. http://dx.doi.org/10.1016/j.dam.2005.03.001.

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44

Blanchet-Sadri, F., C. D. Davis, Joel Dodge, Robert Mercaş, and Margaret Moorefield. "Unbordered partial words." Discrete Applied Mathematics 157, no. 5 (2009): 890–900. http://dx.doi.org/10.1016/j.dam.2008.04.004.

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45

Shallit, Jeffrey. "APPLIED COMBINATORICS ON WORDS (Encyclopedia of Mathematics and its Applications 105)." Bulletin of the London Mathematical Society 39, no. 4 (2007): 702–4. http://dx.doi.org/10.1112/blms/bdm042.

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46

Bóna, Miklós. "Review of Algorithmic combinatorics on partial words by Francine Blanchet-Sadri." ACM SIGACT News 40, no. 3 (2009): 39–41. http://dx.doi.org/10.1145/1620491.1620497.

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47

Clampitt, David, and Thomas Noll. "Naming and ordering the modes, in light of combinatorics on words." Journal of Mathematics and Music 12, no. 3 (2018): 134–53. http://dx.doi.org/10.1080/17459737.2018.1519729.

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48

Allouche, Jean-Paul, and Tom Johnson. "Combinatorics of words and morphisms in some pieces of Tom Johnson." Journal of Mathematics and Music 12, no. 3 (2018): 248–57. http://dx.doi.org/10.1080/17459737.2018.1524028.

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49

Kleshchev, Alexander, and Arun Ram. "Representations of Khovanov–Lauda–Rouquier algebras and combinatorics of Lyndon words." Mathematische Annalen 349, no. 4 (2010): 943–75. http://dx.doi.org/10.1007/s00208-010-0543-1.

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50

Smith, Jonathan D. H. "Finite Codes and Groupoid Words." European Journal of Combinatorics 12, no. 4 (1991): 331–39. http://dx.doi.org/10.1016/s0195-6698(13)80116-3.

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